Sound waves(phase difference) PLS. HELP

[brunettegurl]

sound waves(phase difference) URGENT PLS. HELP

Homework Statement

2 speakers ,in phase, have a frequency of 170Hz [so lambda= 2m; the speed of sound is 340 m/s] As you move along the x axis, where is the sound:
a)a minimum (compared to nearby pts.)
b)a maximum (compared to nearby pts.)

Homework Equations

r2-r1=delta r

The Attempt at a Solution

so for a) i know that there shld be no sound and that occurs the 1st minimum @ lambda/2

so i did r2-r1 =lamda/2
r2=sqrt(64+r1^2) therefore

sqrt(64+r1^2)-r1=2/2

and this is where i am stuck everytime i open it up the r1 gets canceled or i have r1^2-r1=-63 ..i'm supposed to be getting an r1= 31.5 m ..please help

 

[Doc Al]

so i did r2-r1 =lamda/2
r2=sqrt(64+r1^2) therefore

sqrt(64+r1^2)-r1=2/2

So far, so good.

and this is where i am stuck everytime i open it up the r1 gets canceled or i have r1^2-r1=-63

Show how you got this.

 

[brunettegurl]

sqrt(64+r1^2)-r1=2/2
sqrt(64+r1^2)-r1=1[if i move the sqrt over]
64+r1^2-r1 =1^2
r1^2-r1= -63

the other way i did it was
sqrt(64+r1^2)-r1=2/2 [if i take the sqrt ]
8+r1-r1= 1
in the last one r1's cancel leaving me w/8=1

 

[Doc Al]

sqrt(64+r1^2)-r1=2/2
sqrt(64+r1^2)-r1=1[if i move the sqrt over]

OK.

64+r1^2-r1 =1^2

(You didn't square the left hand side properly.)

How about:
sqrt(64+r1^2)-r1=1
sqrt(64+r1^2) = 1+r1
(continue...)

 

[brunettegurl]

so if i continue with your line of thinking
sqrt(64+r1^2) = 1+r1
64+r1^2=1+r1^2
but if i move it over to get the like terms together wouldn't the r1's still cancel??

 

[Doc Al]

so if i continue with your line of thinking
sqrt(64+r1^2) = 1+r1
64+r1^2=1+r1^2

This time you didn't square the right hand side properly.

What's (1 + r1)^2?
(1 + r1)*(1 + r1) = ?

(Work that out.)

 

[brunettegurl]

thank you so much i was beating my head in the whole time and the mistake was so stupid and silly..thanks again